Faithfulness and Componentiality in Metrics*roa.rutgers.edu/files/421-1000/roa-421-hayes-1.pdfc. Ode...

Bruce Hayes September 29, 2000UCLA

Faithfulness and Componentiality in Metrics*

Abstract

The core ideas of Optimality Theory (Prince and Smolensky 1993) have been shown inearlier work (Hayes and MacEachern 1998) to be applicable to the study of poetic meter:metrical data are appropriately analyzed with ranked, conflicting constraints. However,application of OT to metrics still raises problems. First, while OT grammars derive outputs frominputs, metrics is non-derivational, the goal being simply to characterize a set of well-formedstructures. Second, because constraints in OT are violable and conflict, there can be well-formedoutputs that violate high-ranking constraints. Thus, it is not clear when constraint violationsimply unmetricality. Third, there is no criterion for linking constraint violations to metricalcomplexity. Lastly, candidate competitions in OT always yield winners. This implies—falsely—that unmetrical forms should always suggest their own repairs, in the form of thewinning candidate.

A solution to these problems is proposed along the following lines. The well-formedstructures are those that can be derived from a rich base that includes all possible surface forms��

not from constraint violations per se, but from violations of markedness constraints that outrankcompeting Faithfulness constraints. Complexity works similarly, under a gradient conception ofconstraint ranking adopted from Hayes (in press) and Boersma and Hayes (in press). Lastly,unmetrical lines do not suggest a repaired alternative because their derivations “crash.” Crashingresults from componentiality, and occurs when different components of the metrical grammar(Kiparsky 1977) disagree on which candidate should win.

Data are taken from studies of English folk verse by Hayes and Kaun (1996) and Hayes andMacEachern (1998).

* Thanks to Chris Golston, Patricia Keating, Gerhard Jäger, Elliott Moreton, Paul Smolensky, Donca

Steriade, Colin Wilson, and the participants in a Winter 2000 UCLA seminar class for helpful input in thepreparation of this paper. They are absolved, in the usual way, of responsibility for defects.

Bruce Hayes Faithfulness and Componentiality in Metrics p. 2

1. The Problem

The field of generative metrics attempts to characterize the tacit knowledge of fluentparticipants in a metrical tradition. An adequate metrical analysis will characterize the set ofphonological structures constituting well-formed verse in a particular tradition and meter.Structures that meet this criterion are termed metrical. An adequate analysis will also specifydifferences of complexity or tension among the metrical lines. Example (1) illustrates thesedistinctions with instances of (in order) a canonical line, a complex line, and an unmetrical line,for English iambic pentameter.

(1) a. The li- / on dy- / ing thrust- / eth forth / his paw Shakespeare, R3 5.1.29

b. Let me / not to / the mar- / riage of / true minds Shakespeare, Sonnet 116

c. Ode to / the West / Wind by / Percy / Bysshe Shelley Halle and Keyser (1971, 139)

The goals of providing explicit accounts of metricality and complexity were laid out in the workof Halle and Keyser (1966) and have been pursued in various ways since then.

From its inception, generative metrics has been constraint-based: formal analyses consist ofstatic conditions on well formedness that determine the closeness of match between aphonological representation and a rhythmic pattern. The idea that the principles of metrics arestatic constraints rather than derivational rules has been supported by Kiparsky (1977), whodemonstrated that paradoxes arise under a view of metrics that somehow derives thephonological representation from the rhythmic one or vice versa.

The idea that grammars consist of well-formedness constraints has become widespread inlinguistic theory. An important approach to constraint-based grammars in current work isOptimality Theory (= “OT”, Prince and Smolensky 1993), whose basic ideas have been appliedwith success in several areas of linguistics. One might expect that metrics would be easier toaccommodate in the OT world view than any other area, given that metrics has been constraint-based for over 30 years. Surprisingly, problems arise when one attempts to do this.

To begin, OT is, at least at first blush, a derivational theory: it provides a means to deriveoutputs from inputs. But in metrics, the idea of inputs and outputs has no obvious role to play;rather, we want to classify lines and other structures according to their metricality andcomplexity.

Second, OT defines the output of any derivation as the most harmonic candidate, the formcreated by GEN that wins the candidate competition. Thus, in principle, every unmetrical formought to have a well-formed counterpart, an alternative that wins the competition that theunmetrical form loses. But this fails to correspond to the experience of poets and listeners;unmetrical forms like (1)c usually sound wrong without suggesting any specific alternative.

Third, OT employs a conception of constraint violability under which the ranking of aconstraint is only loosely affiliated with its propensity to rule out illegal forms. This is


manifested in two ways. First, it is common for a form to emerge as the output even though itviolates a rather high-ranking constraint. It does so because all other candidates violate evenhigher-ranking constraints. Second, a form can lose the competition because it violates a low-ranked constraint. This happens when it is part of a set of candidates that tie on all of the higher-ranked constraints. 1 Both cases are the result of constraint conflict, arguably the core idea ofOT.

Constraint violability and constraint conflict raise two major questions for the application ofOT to metrics. First, when does violating a constraint make a form unmetrical? Clearly, givenconstraint conflict, we cannot simply translate earlier metrical constraints into OT and assumethat they will necessarily be effective in excluding illegal forms. Second, when does violating aconstraint make a form complex? Because constraints conflict, we cannot assume a priori thatthe ranking of a constraint will correlate in any simple way with the degree of complexity that aviolation contributes. Many forms in language that are perfect nevertheless violate numerousconstraints.

It might be imagined that metrics is somehow different from other areas of language:perhaps unmetricality and complexity are correlated directly with the ranking of the violatedconstraints, with constraint conflict playing no role.2 However, Hayes and MacEachern’s (1998)study, which posits conflicting constraints, exhibits the dissociation of ranking and well-formed/complexity that is characteristic of OT: there are legal (indeed, canonical) versestructures that violate high-ranking constraints, and there are illegal forms that are ruled out bylower-ranking constraints. Moreover, I think it would be quite surprising if metrics turned out tobe different from other areas of language in never showing the effects of constraint conflict.

Summarizing, four problems confront the development of an Optimality-theoretic approachto metrics: (1) non-derivationality; (2) the fact that unmetrical lines do not suggest their ownrepair; (3) the lack of a way of deriving metricality from constraint ranking; (4) ditto forcomplexity. In this article, I propose solutions to these problems, drawn from several sources.

• I adopt a version of OT based on the principle of the Richness of the Base (Prince and�� !��

press), in which the purpose of the grammar is to delimit the set of well-formedrepresentations, rather than derive one set of representations from another.

• I adopt metrical Faithfulness constraints, which are ranked against Markednessconstraints. Such rankings characteristically determine when forms are metrical.

• The stochastic approach to gradient well formedness developed in Hayes andMacEachern (1998), Hayes (in press), and Boersma and Hayes (in press) is adapted toextend the account of metricality to complexity as well.

1 This is essentially the “emergence of the unmarked” phenomenon, documented in McCarthy and Prince

(1994) and much further work.2 This is the view, I believe, adopted in Golston (1998); see also Golston and Riad (2000a, 2000b).


• I assume, following Kiparsky (1977), that the metrical grammar is componential, andthat under OT the representations should be evaluated independently in each component.To be well formed, an output must win the competition for every component. Thispermits grammars that rule out forms absolutely, without suggesting an alternative.

The data with which I will test my proposals involve two problems that (in my opinion)received only partial solutions in earlier work: free variation in quatrain structure (Hayes andMacEachern 1998) and the distribution of mismatched lexical stress in sung verse (Hayes andKaun 1996).

The proposal may be of interest beyond metrics, since the problems at hand—characterizinginventories of well-formed representations, characterizing gradient well-formedness distinctionsamong them, and teasing apart the effects of separate grammatical components—occur widely inlinguistics.

2. Basics

I follow here a number of mainstream assumptions of generative metrics. Specifically, Iassume that a meter forms an abstract rhythmic pattern, and that there exists for each tradition asystem of principles that determine when phonological material properly embodies its pattern inverse. The verse examined here will be the sung verse of traditional Anglo-American folk songs.For many such songs, the rhythmic pattern of each line is can be represented as in (2):

(2) [ x x ] line[ x x ] [ x x ] hemistichs[ x x ] [ x x ] [ x x ] [ x x ] dipods[ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] feet

This is a “bracketed grid” (Lerdahl and Jackendoff 1983, Halle and Vergnaud 1987), whichembodies information about the relative prominence of its terminal positions (height of gridcolumns) and about grouping (constituency at various levels, labeled here at the right side of thegrid). The anonymous poet/composers who collectively created the body of Anglo-Americanfolk song sought (tacitly) to provide phonological embodiments of this and similar structures.They did so by matching the rhythmic beats (grid structure) with syllables and stress; and bymatching the constituent structure with phonological phrasing. A simple example is thefollowing:3

3 Readers seeking help in interpreting the gridded examples may download chanted versions of them (in .wav

format) from http://www.linguistics.ucla.edu/people/hayes/FaithfulnessInMetrics/. Example (3) is rendered inmusical notation in Hayes and MacEachern (1998, 475).



| | | | | | | | | | |It was late in the night when the squire came home Karpeles 1932, #33A

Inspection of this line shows a good match on several grounds: the tallest grid columns are filledwith stressed syllables; most of the shortest grid columns initiate no syllable at all; the syllablesare fairly well matched with their natural durations; and the main prosodic break of the sentence(after night) coincides with the division of the line into two hemistichs. For discussion andexemplification of these phenomena, see Hayes and Kaun (1996).

In English folk songs, it is not just lines that are metrically regulated, but also higher-levelstructures like quatrains. Hayes and MacEachern (1998; hereafter HM) is a study of quatrainstructure, focused in particular on the sequencing of line types within quatrains. For whatfollows, it will be crucial to make use of HM’s typology of line types, which is reviewed below.

A line type that HM call “3” places its final syllable on the 11th grid position—the third ofthe four strongest beats in the line. The extensive empty grid structure that follows this syllableis detectable in the timing of performance. An example, with its grid structure, is given in (4).


| | | | | | |As bright as the sum- mer sun Ritchie (1965), p. 36

G (mnemonically “Green-O”) has elongation of the syllable occupying the third strong beat,with no further syllable initiated until the fourth strong position:


| | | | | | |A- mong the leaves so green O Sharp 1916, #79

3f (“three-feminine”4) has one weakly stressed syllable after the third strong beat and anunfilled fourth beat.

4 In traditional metrics, a “feminine ending” is one in which the penultimate syllable of the line bears stress

and the final syllable is unstressed. Most 3f lines do indeed have this stress pattern in their final two syllables.



| | | | | | | |She’s gone with the gyp- sen Da- vy Karpeles (1932), #33A

4 is a “none of the above” category, with all four strong beats overtly filled and noelongations.


| | | | | | | |The keep- er did a shoot- ing go Sharp 1916, #79

The distribution of these line types within quatrains is restricted. Inspecting a corpus of1028 Appalachian folk songs and other material, HM determined that only certain sequences of3, G, 3f, and 4 lines can constitute a well formed quatrain. The list of types that are well attestedand assumed to be well formed appears below. For examples of these quatrain types, see HM478-82.

(8) 4444 4G4G 444G GG4G G343GGGG 43f43f 4443f 3343 3f3433f3f3f3f 4343 4443 3f3G33333 G3G3 GGG3

3f33f3 3f3f3f3

HM also lay out and defend an Optimality theoretic analysis of their data, which assumes aset of ten metrical markedness constraints.5 The idea is that each quatrain type results from asong-specific ranking of the constraints. The GEN function is assumed to provide all of theconceivable schematic quatrain forms, each represented simply as a sequence of line types, e.g.4343. In verse composition, the poet is assumed to adopt a particular ranking of the markednessconstraints, so that a single quatrain type wins the Optimality-theoretic competition.

The set of possible quatrain types in (8) is modeled by assuming that the poet may freelyrank the constraints for purposes of composing any particular song, but adheres to that rankingfor all of the song’s quatrains. Therefore, the set of quatrains that are predicted to be legal arethose that can be derived by ranking HM’s constraints. In other words, the analysis predicts theinventory of (8) (or something reasonably close to it) as the factorial typology (Prince andSmolensky 1993, Kager 1999) of the constraint set.6

5 There is also one output-to-output correspondence constraint, which requires similar quatrains to occur in

different verses of the same song.6 A slight complication: it is necessary to stipulate that certain constraints are undominated, so that the actual

set of predicted outputs is smaller than the full factorial typology.


3. Problem I: Free Variation in Quatrains

The first empirical problem to be discussed here stems from an inadequacy in the HManalysis: its treatment of free variation. Poets do not always use the same quatrain schemethroughout a multi-quatrain song. The most common pattern of variation (often found inballads) is one in which the poet uses 3 in the even-numbered lines of each quatrain, but either 4or G for the odd-numbered lines, thus (4/G)3(4/G)3.

An example of (4/G)3(4/G)3 is given below in (9), which includes four quatrains taken fromthe same song. Strong metrical beats are marked with underlining and (for silent beats) /∅ /.

(9) 4 Young Edward came to Em-i-ly3 His gold all for to show, ∅ 4 That he has made all on the lánds,3 All on the lowlands low. ∅

G Young Emily in her chám———ber3 She dreamed an awful dream; ∅ 4 She dreamed she saw young Edward’s blóod3 Go flowing like the stream. ∅

G O father, where’s that strán———ger3 Came here last night to dwell? ∅G His body’s in the ó——cean3 And you no tales must tell. ∅

4 Away then to some councillor3 To let the deeds be known. ∅G The jury found him guíl———ty3 His trial to come on. ∅ Karpeles 1932, #56A

HM note (pp. 490-492) that the purpose of this variation is almost certainly to permit awider variety of word choice on the poet’s part. The poet’s choice of 4 vs. G is based on thestress pattern of the last two syllables of the line: G for / ... σ� σ / and 4 for other line endings.This dependency is illustrated by the boldface material in (9). Moreover, general principles ofmetrics, involving the matching of rhythmic pattern with linguistic stress (see Halle and Keyser1971, Kiparsky 1977, Hayes 1989, and Hayes and Kaun 1996) would in fact lead us to expectjust this distribution.

The issue of how to derive the free variation in (4/G)3(4/G)3 is deferred by HM. As astopgap, they propose “F” as a fifth line type, defined specifically as involving free variationbetween 4 and G. To this they add a MATCH STRESS constraint, whose effect is specifically tofavor F. Under this arrangement, it is possible to derive quatrain types like (4/G)3(4/G)3, viewedas “F3F3,” simply by ranking MATCH STRESS high enough.


A more principled account would allow each of the types in {4343, G343, 43G3, G3G3} toemerge as a winner of the candidate competition under appropriate circumstances, relating to thestress pattern of the line ending, and hence ultimately to the poet’s choice of words. However,such a capacity is beyond the HM system, since that system only evaluates schematicrepresentations like “4343”, without regard to their linguistic content.

At this point, we can state the problem to be solved: to set up a grammatical system thatuses authentic structural elements rather than artificial constructs like F, and which can derivevariable quatrain types like (4/G)3(4/G)3. This will require us first to develop the formalapparatus.

4. Theory

4.1 The Uses of OT Grammars

To begin, it is helpful to consider what Optimality-theoretic grammars can do.

The most familiar function is that of derivation. For instance, from a phonologicalunderlying representation, we seek to derive the surface representation. The way in which this isdone is now widely familiar: a GEN function creates all conceivable surface representations,and the output is selected from among them by successively winnowing down the candidate setthrough a ranked set of constraints until one winner emerges.

A second thing that OT grammars can do is inventory definition: the definition of a fixed(though possibly infinite) set of legal structures. The method of inventory definition describedhere is based on Prince and Smolensky (1993), Smolensky (1996), and the work of Keer and�� "��#��$��%�� &'(�

called GENrb (“GEN of the Rich Base”) that defines the full set (possibly infinite) of underlyingrepresentations. Submit each member of GENrb to an OT grammar. When this is done, it willoften be the case that distinct members of GENrb will be mapped onto the same surface form.Assume further a process of collation: we remove duplicate outputs, and thus collect the full setof forms that are derived as an output from at least one input. This is the inventory that thegrammar defines. I will call this inventory the output set, and I will refer to an Optimality-theoretic grammar intended for defining an output set as an inventory grammar.

If we allow GENrb to be sufficiently unconstrained, then it will generate everything that is inthe traditional GEN, the GEN that creates surface candidates. This raises the possibility thatlegal surface forms could be derived from underlying representations to which they are identical.Such derivations, though trivial in form, are hardly trivial in their consequences, since the pointof interest here is not the derivations themselves, but the output set that emerges.

In this approach, the primary function of an inventory grammar is essentially that of a filter:the output set is the input set as filtered down through the neutralizations induced by thegrammar. This is illustrated schematically in the diagram below:


(10) • • • • • • • • • • • • • • • GENrb

• • • • • • • output set

Characterizing inventories of possible outputs is of course a common goal in generativelinguistics. The set of phonologically legal words is one such inventory, and Hayes (to appear)and Prince and Tesar (to appear) use the method just described to define this set. OT syntax issometimes taken to involve derivation of sentences from their logical forms; however, thecommonplace occurrence of logical forms that have no felicitous syntactic expression (such asthe logical forms for island-violation sentences) suggests that work might better be directedtowards developing inventory grammars, which define an output set of form-meaning pairs.7

4.2 Inventory Grammars and Faithfulness

An important part of an inventory grammar will be the Faithfulness constraints, which play acrucial role in determining which forms make it into the output set, despite their violations ofcompeting Markedness constraints. The conflict between Faithfulness and Markednessconstraints is of course a central idea of derivational OT. This holds true as well for inventorygrammars in the present conception. However, for inventory grammars the derivations are onlyof interest for the output set that they define.

In fact, there is an important class of cases in which the only derivations that need beexamined at all are the trivial ones in which input and output are identical. Suppose that theinventory grammar at hand is transparent, in the sense of Kiparsky (1971). Under thiscircumstance, any output that can be derived at all can be derived from an underlyingrepresentation identical to itself. The diagram in (10) above shows a transparent grammar; everyoutput set member is dominated by a vertical arrow, showing that the form can be “derived fromitself”. Opaque grammars have output set members derivable only with a “diagonal” derivation,shown in (11):

(11) • • • • • • • • • • • • • • • GENrb

• • • • • • • output set

The opacity here is seen in the first point in the output set, which can be derived, but not fromitself—the corresponding input is mapped onto a distinct output.

7 .HHU DQG %DNRYLü �� %DNRYLü DQG .HHU� LQ SUHVV� ZHUH WR P\ NQRZOHGJH WKH ILUVW WR GHYHORS WKH

conception given here of an OT grammar as a device that filters, rather than builds, representations. My approach isLQGHEWHG WR WKHLU ZRUN� EXW , EHOLHYH WKDW LW JRHV D VWHS IXUWKHU� .HHU DQG %DNRYLü DGRSW� DW OHDVW LPSOLFLWO\� WKH YLHZ

that any underlying form (for them, a logical form) necessarily gives rise to some surface form (a syntacticstructure). Thus, derivations never crash; they just yield outputs that differ from the input. But the hardest cases tohandle, as the main text notes, are logical forms that have no legal syntactic expression.

As will be seen below, I treat the analogous problem in metrics by deploying grammatical components in away that causes derivations to crash. It remains to be seen if this approach would work for syntax and semantics.


Real phonologies probably have cases of this sort. A possible instance is: /a/ → [e], /e/ →[i] in some context, so that a form containing [e] in the relevant context can be derived, but notfrom itself.8 But other grammatical systems, including metrics and syntax, probably do notinvolve opacity. For such systems, a simple grammaticality test is available for any form: feedit into the grammar as an input; if it emerges unaltered, then it is part of the output set. In thisarrangement, the grammar is clearly acting as a filter.

In this conception, “Faithfulness” comes to mean something rather different from what itdoes in OT-as-derivation. For “filtering” systems, Faithfulness constraints essentially assert thata given property can exist in the output set, even where there are Markedness constraints thatmilitate against it—the crucial condition is that Faithfulness must outrank Markedness. Thehigher the Faithfulness constraints, the more inputs will survive unfiltered as outputs. Fordiscussion of this property of OT grammars, see Smolensky (1996).

4.3 Metrics with Inventory Grammars

HM was an attempt to do metrics with an inventory grammar. However, all the constraintsin their grammar were Markedness constraints, so the concepts of input forms and Faithfulnesswere irrelevant. To solve the problem we are addressing (from §3), we need to use inventorygrammars that include Faithfulness constraints.

I propose that the set of legal quatrains, under a particular constraint ranking, should bedefined as the output set for that constraint ranking. Moreover, the candidate set does not consistof schematic quatrain forms like “4343”, as in HM, but rather quatrains fully embodied inphonological material. To give an instance, the first quatrain in (12) can be taken to be arepresentative input form: 9


| | | | | | | |Young E- mi- ly in her cham- ber

[ x x ] line[ x x ] [ x x ] hemistichs[ x x ] [ x x ] [ x x ] [ x x ] dipods[ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] feet

| | | | | |She dreamed an awful dream

8 For general discussion of such shifts, see Kirchner (1996). A specific example from Basque is given in

Kenstowicz and Kisseberth (1979, 176-177), based on de Rijk (1970).9 An expository simplification: phonological representations are depicted as orthography, without stress or

phonological phrasing.



| | | | | | | |She dreamed she saw young Ed- ward’s blood


| | | | | |Go flowing like the stream Karpeles 1932, #56A

Assuming that metrics is transparent, this candidate will count as well-formed (i.e. metrical) if itpasses the well formedness test for inventory grammars. Specifically, when we adopt this formas an input, it should win the Optimality-theoretic competition against all other candidates, sothat it is “derivable from itself”. A major advantage that candidate (12) possesses in thiscompetition is that all other candidates will incur Faithfulness violations.

4.4 Componentiality in Metrics

Before examining the candidate competition, we must add one more ingredient to theanalysis: the role of components in candidate evaluation. The issue of componentiality inmetrics is taken up by Kiparsky (1977), whose conception is adopted here. The followingsections review Kiparsky’s proposal.

4.4.1 Pattern Generator

A component of pattern generating rules defines the rhythmic pattern with whichphonological material is set in correspondence, i.e. the meter. In the present case, the rhythmicpattern is rather simple, and in OT we can characterize it with a set of undominated constraints:

(13) a. Quatrain = Couplet Coupletb. Couplet = Line Linec. Line = Hemistich Hemistich

xd. Hemistich = [x x ] where terminals are Dipod heads

xe. Dipod = [x x ] where terminals are Foot heads

xf. Foot = [x x ] where terminals are metrical positions

These constraints yield the following structure: [Quatrain [Couplet Line Line ] [Couplet Line Line ] ],where each Line has the internal structure given above in (2).


4.4.2 Prosodic Rules/Paraphonology

Kiparsky also assumes a component of prosodic rules, which serve to define thephonological representations that are used in composing verse. These rules “constitute aparalinguistic system that specifies the poetic language as a derivative of the system ... ofordinary language” (Kiparsky 1977, 241). For example, one of the prosodic rules found in theverse of John Milton deletes stressless vowels postvocalically:

(14) Postvocalic Syncope (Kiparsky 1977, 240-241)

− stress

V → ∅ / V ___

The rule applies optionally, as we can see for instance by the appearance of riot in ParadiseLost as either one or two syllables (15), and of variety as either three or four (15):

(15) a. Of riot / ascends / above / thir lof- / tiest Towrs PL 1.499To lux- / urie / and ri- / ot, feast / and dance PL 11.715

b. For Earth / hath this / vari- / ety / from Heav’n PL 6.640Varie- / tie with- / out end; / but of / the Tree PL 7.542

Specifically, the paraphonology derives monosyllabic [�ra�t] from disyllabic /�ra�.��/, andtrisyllabic [v�.�ra�.ti] from quadrisyllabic /v�.�ra��ti/. Examples of this type are found inShakespeare as well. As Kiparsky points out, no examples occur in Pope’s verse, which showsthat Postvocalic Syncope is poet-specific.

Since we will be assuming an Optimality-theoretic view of phonology in which there are norules, Kiparsky’s original term for this component is inappropriate here, and we will adaptanother of his terms for the purpose: the auxiliary system that specifies the phonologicalrepresentations for poetry will be called the paraphonology.

It is straightforward to translate Kiparsky’s prosodic rules into Optimality-theoretic terms;for instance, Postvocalic Syncope reduces to something like the following:10

(16) a. ONSET is freely ranked against

b. MAX

−+

stresssyllabic

Where ONSET dominates, the stressless vowel will be dropped from riot in order to avoid the

onsetless second syllable; where MAX

−+

stresssyllabic dominates, the vowel will be retained.

10 For ONSET, see Prince and Smolensky (1993); for MAX( ), see McCarthy and Prince (1995).


A point that will be crucial below is that, at least in English, paraphonology has only modesteffects: schwas are lost in hiatus, nonlow vowels become glides, but major insertions anddeletions (say, of whole syllables) are not found. References on English verse paraphonologysupporting this point include Bridges (1921) and Tarlinskaya (1973). I will also assume, forreasons to be given below, that paraphonology cannot alter the stress patterns of words. Thismeans that when the data show a mismatch of stress against the grid, I will be assuming that thisinvolves a Markedness violation in the metrics proper, not a Faithfulness violation in theparaphonological component.

4.4.3 Comparator

The last part of the componential organization that Kiparsky assumes is the comparator.This is the core of the metrical system. It consists of a set of metrical filters (essentially,constraints), which input a phonological representation from the paraphonology and a rhythmicrepresentation from the pattern generating component, and determine whether and how they canbe matched to form a line (or quatrain, or whatever) of metrical verse. Further principlesadumbrated by Kiparsky assign differences of complexity among metrical lines.

4.4.4 Componential Organization and the Evidence Supporting It

The overall componential organization of the system (Kiparsky 1977, 190) is as follows:

(17) pattern phonologicalgenerator component

basic metrical phonologicalpatterns derivations

metrical comparator paraphonologyrules derived metrical metrically relevant

patterns range of phonologicalrepresentations

metrical analysis:(a) possible scansions(b) degree of complexity

An important contribution of Kiparsky’s work is to provide empirical arguments that theorganization of metrics is indeed componential. The most crucial idea is that the paraphonologyalways provides the same representation to every metrical constraint: for example, constraintsmatching stress cannot regard riot as monosyllabic while constraints matching syllable count torhythmic positions regard it as disyllabic.

In an Optimality-theoretic account of the metrical paraphonology, there is an additionalreason why the system must be componential. In OT, structural changes (for example, vowelloss) are decoupled from their phonotactic causes (for example, the requirement that syllables


have onsets). A non-componential theory of paraphonology would wrongly claim that structuralchanges could be triggered in order to obey the requirements of the metrics.

Here is a hypothetical example. Imagine we are dealing with the verse of a poet like Miltonwho licenses loss of stressless vowels in postvocalic position. It is necessary under any accountof metrics to assume a constraint that prevents extra syllables from cropping up in randomlocations in the iambic pentameter line; let us call this constraint *UNGRIDDED σ. If the systemis not componential, we would expect to find lines like this:

(18) *Vivacity without end; but of the Tree (construct)

This would follow from the constraint ranking given in (19)a, with representations as in(19)b:

(19) a. *UNGRIDDED σ >> MAX

−+

stresssyllabic

[metrical constraint] [paraphonological constraint]

b. [ x x ] line[ x x ] [ x x x ] hemistichs[ x x ] [ x x ] [ x x ] [ x x ] [ x x ] feet

| | | | | | | | | |[v� �væs<�>ti] without end; but of the tree

To my knowledge, such cases do not exist. Paraphonological phenomena in metrics alwayshave authentic phonological structural descriptions. Indeed, as Kiparsky points out, they lookjust like ordinary language phonology, and are often grounded in the fast-speech phonology ofthe poet’s language. A componential organization of the metrical system implies, correctly, thatparaphonological processes apply only when their phonological structural descriptions are met.

4.4.5 Defining Metricality in a Componential Inventory Grammar

With the concepts of inventory grammar and componentiality in place, we can define howthe metrical system works. The leading idea, found in earlier work such as Inkelas and Zec(1990), is that different components simultaneously evaluate the well formedness of the samerepresentation.11 The components are separate not because they apply in sequence, but becausethey evaluate different aspects of the representation.

Following this approach, we can say that a quatrain of verse is metrical when the followingconditions are met:

11 For other conceptions of componentiality in OT, see Pesetsky (1997, 1998), Blutner (forthcoming), Jäger

and Blutner (forthcoming), and Wilson (in press).


(20) Metricality

A verse form is metrical iff

a. The metrical pattern belongs to the output set for the grammar governing metricalpatterns (§4.4.1).

b. The phonological material belongs to the output set for the paraphonology (§4.4.2).c. The complete representation, with phonological material aligned to the metrical pattern,

belongs to the output set for the grammar of metrical correspondence (§4.4.3).

Componentiality guarantees the result observed in the previous section: paraphonologycannot be conditioned metrically, because the candidate set against which forms areparaphonologically evaluated consists solely of phonological representations, without regard totheir metrical setting. Thus, if a schwa is lost paraphonologically, it must be lost in order toavoid a hiatus, rather than to avoid a mismatch in the scansion—if a mismatch happens to beavoided, that is a felicitous result for the poet, but the components of the metrical grammar actblindly to each other’s purposes.

As will become clear below, the componential approach is also crucial to explainingmetricality. It introduces the possibility that the rival candidates that defeat an input aresometimes ill-formed with respect to some other component, specifically the paraphonology.This is the crucial means by which lines may be classified as unmetrical.

In the sections that follow, I demonstrate how lines are classified as metrical or unmetricalin this system. Once this is done, we can return to the problem that was stated in §3, the(4/G)3(4/G)3 quatrain.

5. Unmetricality in 4343 Quatrains

Many English folk songs (particularly ballads) are composed in quatrains of the form 4343.By this I mean that the odd-numbered lines in these songs are consistently of the type 4, andnever G. Since ballads can go on for many stanzas, we can be confident that in such cases, thequatrain structure is not the (4/G)3(4/G)3 discussed in §3 above. A quatrain of the type 43G3,G343, or G3G3 introduced into a strict 4343 song would be considered ill formed, forming anunlicensed deviation from the established meter. The present task is to develop atricomponential, Optimality-theoretic inventory grammar that permits only 4343.

5.1 Outline of the Analysis

The bulk of the work will be done in the metrics proper, i.e. Kiparsky’s “Comparator”; andall constraints mentioned should be assumed to belong to this component unless otherwise stated.The metrical constraints that will be used here are all given in HM, pp. 483-494. I will omit allbut the most cursory discussion of the constraints themselves, referring the reader to HM for afull account.

The full candidate set is enormous, since it comprises all phonological representationsplaced in correspondence with the grid (see §4.3). However, for initial purposes it suffices to use


formulae like “4343” to designate any quatrain at all that would be classified as 4343. Classifiedin this way, the candidate set numbers 256, which is the set of logical possibilities implied bychoosing from among four line types, four times per quatrain (256 = 44).

To preview the analysis in rough form, the candidate set is culled down to a single winner asfollows (see (21)b for an illustrative tableau):

• The constraint COUPLETS ARE SALIENT (HM 485-6, 492-3) is non-minimally violated by247 of the 256 candidate types. This constraint is non-minimally violated when thecouplet terminates in any line type other than 3, or else begins with a 3. See HM fordiscussion of how these patterns relate to the intuitive notion of perceptual salience.Thus, only nine candidate types survive the first round of the competition.

• Of these nine, four maximally satisfy the constraint FILL STRONG (HM 490), whichrequires the four strongest positions in the line to be filled with syllables. This constraintis violated whenever a line of type 3f or 3 occurs in the quatrain.

• Of these four, only candidates of type 4343 maximally satisfy the constraint *LAPSE (HM490), which assesses a violation whenever no syllable occurs between two strong gridpositions. *LAPSE is violated by any line of type G or 3.

It emerges that under the ranking summarized in (21)a, 4343 will always be the winningcandidate:

(21) a. Ranking

COUPLETS ARE SALIENT >> { FILL STRONG, *LAPSE } >> other constraints

b. Tableau

/4343/ CO

UPL

ET

S

AR

E S

AL

IEN

T

FIL

L S

TR

ON

G

*LA

PSE

OT

HE

R

CO

NS

TR

AIN

TS

� [4343] ** ** (*)*[G343] ** ***! (*)*[43G3] ** ***! (*)*[G3G3] ** ***!* (*)*[3f343] ***! ** (*)*[433f3] ***! ** (*)*[G33f3] ***! *** (*)*[3f 33f3] ***!* ** (*)*[3f3G3] ***! *** (*)

247 candidates *!(*) (*) (*) (*)


5.2 Ruling out Unmetrical Forms: A Scenario

What must now be demonstrated is that this analysis is effective in ruling out unmetricalquatrains, under the conception of metrical grammar laid out in §4 above. Here, we must movebeyond schemata like 4343 to actual candidate quatrains.

Suppose that the anonymous folk poet is making up a new stanza for a ballad.12 Assumethat this ballad (like hundreds of others) is composed in strict 4343 quatrains. We mustdemonstrate that under the grammar of (21)a, any other quatrain type would emerge asunmetrical.

Here is an example. It is easy to imagine that a poet composing in 4343 might brieflyponder a G343 quatrain instead. For concreteness, suppose that the first line of this candidatequatrain happens to be identical to the first line of (12) above; repeated for convenience in (22):


| | | | | | | |Young E- mi- ly in her cham- ber

Although this line does appear in a real song composed in (4/G)3(4/G)3, and is thus metrical inits own context, it could not metrically appear in a song composed in strict 4343.

What we want the analysis to predict is that in a strict 4343 context, a quatrain with (22) asits first line is unmetrical. The poet who has pondered it as a possible line will intuitively feelthat it doesn’t sound right, reject it, and think of something else.

The folk poet is assumed to have (tacitly) internalized an inventory grammar, of which (21)aabove is a partial sketch. I will assume without proof that this grammar is transparent. Underthis assumption, one can show that (22) is unmetrical in the given context by using the“grammaticality test” laid out in §4.2. Specifically, one must demonstrate that when (22) isadopted as an underlying representation, there will be a rival candidate that defeats (22) in thecandidate competition. However, before doing this, I must first describe the Faithfulnessconstraints assumed to be present in the grammar of metrical correspondence.

12 This scenario glosses over what actually happens in folksong composition. An extensive scholarly

literature (e.g. Sharp 1907, Abrahams and Foss 1968, Karpeles 1973) provides a more accurate picture. Folk songsare collectively composed and imperfectly transmitted, with new variants constantly introduced. These variants canbe taken up into the tradition, and transmitted further in an ever-changing mix. The changes contributed by any oneindividual are usually minor.

There are, however, clear cases where a folk poet can be said to be engaged in wholesale verse composition.These occur in a type described by Abrahams and Foss (1968, 34): new words are invented to an old tune, toproduce a ballad about some recent contemporary event. Here, the folk poet clearly must make up new verses to anexisting quatrain pattern.


5.3 Excursus: Two Faithfulness Constraints

For present purposes, it suffices to include just two Faithfulness constraints:

(23) a. MAX(σ): Assess a violation for every syllable in the underlying form that is not in correspondence with a syllable in the surface form.

b. DEP(σ): Assess a violation for every syllable in the surface form that is not incorrespondence with a syllable in the underlying form.

These constraints are stated in the language of Correspondence Theory, developed in McCarthyand Prince (1995).

It is straightforward to determine the MAX(σ) and DEP(σ) violations for any pair of inputand output, when they are classified by their line type (see (4)-(7) above). For example, 4 has anextra syllable with respect to G, and therefore candidates that are classified as 4 incur a DEP(σ)violation when the underlying representation is classified as G.13

We can now include MAX(σ) and DEP(σ) among the “other constraints” of grammar (21)b,which now looks like (24):

(24) COUPLETS ARE SALIENT >> { FILL STRONG, *LAPSE } >> { MAX(σ), DEP(σ), all remainingconstraints }

5.4 Completing the Analysis

To complete the analysis, we need to find a rival candidate that, under the ranking of (24),will defeat (22) in the competition, and therefore prove it unmetrical. There are many suchcandidates, one of which is shown in (25):


| | | | | | | | |Young Em- i- ly in her [�t�e�m b� l�]

The reader is asked for the moment to ignore the absurdity of the word chambeler andconcentrate solely on the candidate competition. Candidate (25) violates DEP(σ), since itpossesses a syllable [b�� where the input form (22) has a null. However, there is also amarkedness constraint that is violated by (22) but not (25): *LAPSE, which is violated by all

13 More precisely, at least one DEP(σ) violation, since there may be more than one “extra” syllable in the 4

line. The distinction will not be crucial here.


cases of G but not by 4. Since in grammar (24) *LAPSE dominates DEP(σ), then (25) will emergeas more harmonic than (22):

(26) input form: (22) Young Emily in her cham——ber *LAPSE DEP(σ)� (25) Young Emily in her chambeler ** (22) Young Emily in her cham——ber *!

As (26) shows, (22) is defeated in the candidate competition, despite its obvious Faithfulnessvirtues. It is excluded from the output set of the grammar defined by this constraint ranking, andtherefore is unmetrical in its context.

The reader will have noticed that candidate (25) is itself absurd from a different point ofview: nothing in the paraphonology of English folk verse licenses the extra syllable, or theinserted segmental material [�l]. Here, componentiality plays a crucial role. Candidate (25) doesnot directly compete with (22) with regard to its phonological content; that competition unfoldswithin the paraphonological component—where (25) most definitely loses.14 But under thecomponential definition of metricality under (20), the winner must belong to the output set ofeach component separately, and therefore must defeat all rivals in each component separately. Inthe grammar under discussion, (22) fails to defeat (25) in the Comparator component; i.e. themetrics proper. The fact that its phonological material wins the paraphonological competitioncannot rescue (22).

Consequently, for the grammar of (24) and the underlying representation (22), there is nocandidate that wins in all components. For this reason, (22) is excluded outright— the derivation“crashes,” and the input form is classified as unmetrical.

One might appropriately call the “chambeler” line (25) a suicide candidate. In acomponential inventory grammar, a suicide candidate is one that defeats the maximally-faithfulcandidate in one component, while losing to the faithful candidate in a different component.Suicide candidates usually cause derivations to crash.15

A consequence of crashing derivations is that a grammar can predict a line to be ill formedwithout making any claims about which more optimal form should putatively take its place. In

14 Specifically, since*[ªt6e,mb�l¶] includes segments [�] and [l] that are absent in its lexical representation

/¥t5e,mb¶/, it violates the paraphonological Faithfulness constraints DEP(�) and DEP(l). It also obeys no constraintsthat I can imagine that are not also obeyed by [ªt6e,mb¶@. Therefore, any quatrain including *[ªt6e,mb�l¶] is alwaysparaphonologically defeated by a candidate containing [ªt6e,mb¶@, no matter how the constraints of theparaphonology are ranked.

Substituting a real word like featherbed for chambeler does not help, since the paraphonology must construe[¥f'&¶©b'd] not as the word featherbed but as a candidate surface representation for underlying /¥t5e,mb¶/; it plainlycannot win the paraphonological competition.

15 The derivation does not crash when a third candidate exists that wins in all components. Such casesnevertheless cause the input to be designated as unmetrical.


the case of (22), there simply is no alternative line that emerges from the grammar as theappropriate “corrected” version: any alternative that beats (22) metrically will beparaphonologically impossible. We can imagine that the folk poet who ponders introducing (22)into a song composed in strict 4343 might intuitively sense that a syllable is missing, more orless where the [b�] syllable of (25) occurs. But the grammar does not tell the poet what thissyllable should be; indeed, the reaction of the poet at this point plausibly would be that nothingworks here, and that it is time to think up a different line.

5.5 Local Summary

We have seen that a G343 quatrain appearing in a strict 4343 context is unmetrical notsimply because the crucial Markedness constraints (*LAPSE) is highly ranked. Rather, it isbecause *LAPSE dominates the crucial Faithfulness constraint (DEP(σ)) that would permit a G343quatrain to survive the candidate competition.

More generally, songs can be written in strict 4343 because, under the appropriate ranking,there is no Faithfulness constraint that is ranked high enough to permit any quatrain type otherthan 4343 to win. To give one further example, *4344 is impossible in a 4343 song because theFaithfulness constraint MAX(σ) (which favors 4344 when it is the underlying form) is dominatedby COUPLETS ARE SALIENT (which favors 4343). Any underlying form of the type 4344 willalways lose to a suicide candidate that drops the final syllable(s) of the final line, thus forming4343. Therefore, the answer proposed here to the question asked in the introduction—Whendoes violating a constraint make a form unmetrical?—is that it depends on the ranking of thatconstraint relative to the Faithfulness constraints that protect the form.

We have also seen an answer to a further questions asked in the introduction: How canunmetrical forms sound wrong without suggesting any specific alternative? The answer is thatunmetricality results from more than just losing the constraint competition within the metricsproper. When a form loses the competition to a rival that itself loses in another component, thenthere will be no overall winner.

6. Deriving Free Variation

We now have the apparatus needed to deal with the problem laid out in §3: deriving the(4/G)3(4/G)3 quatrain. The crucial idea will be that in the grammar for (4/G)3(4/G)3, therelevant Faithfulness constraints—MAX(σ) and DEP(σ)—are ranked higher than they are in thegrammar for 4343. This permits a larger output set, which encompasses the free variants.

The specific ranking needed is the one given in (27). This ranking differs from the earlierranking for strict 4343 in (24) in that the constraints MAX(σ) and DEP(σ) this time outrank*LAPSE:

(27) COUPLETS ARE SALIENT >> FILL STRONG >> { MAX(σ), DEP(σ) } >> {*LAPSE, remainingconstraints}

A tableau for the variant 43G3 is given in (28).


(28) /43G3/ CO

UPL

ET

S AR

E

SA

LIE

NT

FIL

L S

TR

ON

G

MA

X( σ

)

DE

P ( σ)

*LA

PSE

LIN

ES A

RE

SA

LIE

NT

LO

NG

-LA

ST

� [43G3] ** *** 11016 **[4343] ** *! ** 200 *

*[G3G3] ** *! **** 20 **[G343] ** *! * *** 110*[3f343] ***! * * ** 101*[3f3G3] ***! * *** 11*[433f3] ***! * * ** 101 **[G33f3] ***! ** * *** 11 **[3f33f3] ***!* ** * ** 2 *

247 candidates *!(*) (*) (*) (*) (*) (*) (*)

Grammar (27) culls the rival candidates in a way similar to the 4343 grammar (21): COUPLETS

ARE SALIENT removes 247 of the 256 candidate types, and FILL STRONG removes five of theremaining nine. Thus, at this point we know that the output cannot contain any quatrains otherthan the four targets; what is at issue is whether all four will make it into the set.

Grammar (27) differs from grammar (21) in the following crucial way: instead of placingthe Faithfulness constraints at the bottom of the hierarchy, (27) places them just below FILL

STRONG, so that they are active in selecting from among the surviving four candidates. When theunderlying representation is a 43G3 quatrain, any rival candidates of the types 4343, G3G3, orG343 will incur Faithfulness violations. The 43G3 form, being totally faithful to itself, thusemerges as a winner and hence qualifies as a member of the output set.17

Not surprisingly, the three other types embodied in the formula (4/G)3(4/G)3 also emerge aspart of the output set, since each is free of Faithfulness violations when it is selected as theunderlying form. Tableaux showing how each one beats out its three best rivals are given below:

16 The rather obscure-looking numbers for constraint violations in this column implement a scheme laid out

in Prince and Smolensky (1993, §5.1.2.1), which permits a single constraint to handle different degrees of violation(there is a multi-valued scale of line saliency) in multiple locations (there are four lines in a quatrain). I have alsotried the alternative approach, of setting up multiple constraints each defining a cutoff point on the scale, and foundthat it also leads to a working analysis. For details of the numerical scheme, see HM 493 andhttp://www.linguistics.ucla.edu/people/hayes/quattabl.htm.

17 Note that the Faithfulness constraints are crucial for deriving the 43G3 variant. This is because grammar(27) contains Markedness constraints that are ranked below Faithfulness (*LAPSE, LINES ARE SALIENT, LONG-LAST), and these constraints each favor one of the other three contending outcomes.


(29) a. /4343/ CO

UPL

ET

S

AR

E S

AL

IEN

T

FIL

L S

TR

ON

G

MA

X( σ

)

DE

P ( σ)

*LA

PSE

LIN

ES A

RE

SA

LIE

NT

LO

NG

-LA

ST

� [4343] ** ** 200 **[43G3] ** *! *** 110 **[G3G3] ** **! **** 20 **[G343] ** *! *** 110

b. /G343/ CO

UPL

ET

S

AR

E S

AL

IEN

T

FIL

L S

TR

ON

G

MA

X( σ

)

DE

P ( σ)

*LA

PSE

LIN

ES A

RE

SA

LIE

NT

LO

NG

-LA

ST

� [G343] ** *** 110*[4343] ** *! ** 200 *

*[G3G3] ** *! **** 20 **[43G3] ** *! * *** 110 *

c. /G3G3/ CO

UPL

ET

S

AR

E S

AL

IEN

T

FIL

L

MA

X( σ

)

DE

P ( σ)

*LA

PSE

LIN

ES A

RE

SA

LIE

NT

LO

NG

-LA

ST

� [G3G3] ** **** 20 **[4343] ** *!* ** 200 **[43G3] ** *! *** 110 **[G343] ** *! *** 110

6.1 Distribution of 43G3

The 43G3 quatrain type has an interesting property: although there are songs composed in“strict” (non-varying) 4343, strict G343, and strict G3G3 (see HM 478-81), to my knowledgethere are no songs composed in strict 43G3. 43G3 occurs only as a free variant in songs that alsoallow 4343, G343, and G3G3 in other stanzas.

This is predicted by the system given here. There exist rankings (see HM 495) that permitonly 4343, only G343, and only G3G3 to survive into the output set. For these rankings, theoutput set is culled down to a single quatrain type by Markedness constraints placed at the top ofthe ranking. But for 43G3 to survive into the output set, the Faithfulness constraints DEP(σ) andMAX(σ) must be ranked relatively high. When such a ranking holds, then the other three


quatrain types will also be allowed into the output set, since the Faithfulness constraints will notpenalize them when they are selected as the underlying representation.

6.2 Local Conclusion

This concludes the analysis of free variation in quatrain structure. The crucial idea has beenthat when Faithfulness is ranked higher in the grammar, a variety of underlying forms are able todefeat all their rivals and emerge as outputs of the inventory grammar. In this way, the analysisis able to derive free variation, without (as in HM) stipulating constraints that actively require it.

7. Problem II: Lexical Inversion

As a second illustration of Faithfulness and componentiality in metrics, I will discuss aproblem that was addressed but not fully solved by Hayes and Kaun (1996, hereafter HK).

I define a “lexical inversion,” following earlier work, as a configuration in which thesyllables of a simplex polysyllabic word with falling stress are placed in a metrical position thatcalls for rising stress. Here is an example, highlighted in bold:


| | | | | | | |He pulled rings off of his fin- gers Karpeles 1974, 7G

HK noticed that lexical inversions in folk verse have an asymmetrical distribution, which isstrikingly different from what occurs in iambic pentameter. For folk verse, the great majority ofinversions occur at the end of a line, as in (31):18

(31) a. Who should ride by but Knight William Karpeles 1974, 27Ab. I’ll bet you twenty pound, master Karpeles 1974, 7Fc. I fear she will be taken by some proud young enemy Karpeles 1974, 45Ad. There lived an old lady in the north country Karpeles 1932, 5Be. And two of your father’s best horses Karpeles 1932, 5Bf. But he had more mind of the fair women Ritchie 1965, p. 36

g. Lived in the west country ∅ Karpeles 1974, 43E

18 A spreadsheet containing randomly-collected examples of lexical inversion from Anglo-American folk

song is posted at http://www.linguistics.ucla.edu/people/hayes/FaithfulnessInMetrics/. Of the 64 inversions whosesongs use the grid of (2), 58 (= 90.6%) are in line-final position. The exceptions mostly fall under the categoriesdiscussed in HK, 291-294.

The near-strict limitation of inversion to final position indicates that inversion should not be explained byallowing the paraphonology to alter stress pattern. If this were so, we would expect inversion to occur equally oftenin all contexts, given that paraphonological rules cannot “see” the meter.


Most of these are of line type 4 (as in (31)a-f), with a few cases of 3 (as in (31)g). Lexicalinversion is not defined for the G and 3f line types, which actually require a falling stress at theend of the line.

A further asymmetry that HK note is that, where 4 or 3 occur in free variation with G or 3f,lexical inversion is quite unusual. Thus, songs in 4343 include lexical inversions far more oftenthan songs in (4/G)3(4/G)3 quatrains.19

HK propose an intuitive explanation for these facts, which I will here employ as the basis ofan OT analysis. There are three points at issue: (a) why lexical inversion is disfavored ingeneral; (b) why it has a special privilege of occurring at the end of the line, and (c) why thisprivilege should be so rarely exercised in line positions that permit (4/G) free variation.

7.1 Ruling Out Inversion in General

For the first point, HK observe that folk verse virtually always leaves a certain number ofgrid positions unfilled. Therefore, when the syllables of a line are such that an inversion mightarise, it is usually the case that a minor shift in the location of the syllables would make inversionunnecessary. For example, instead of producing the inversion in (32)a (mismatched stress andgrid columns shown in boldface), the folk poet can sidestep the problem simply by movingWilliam over a bit, as in (32)b:

(32) a. [ x x ] line[ x x ] [ x x ] hemistichs[ x x ] [ x x ] [ x x ] [ x x ] dipods[ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] feet

| | | | | | | |*Wil- liam he was a noble knight (construct)

b. [ x x ] line[ x x ] [ x x ] hemistichs[ x x ] [ x x ] [ x x ] [ x x ] dipods[ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] [ x x ] feet

| | | | | | | |Wil- liam he was a noble knight (construct)

To formalize this idea, we need to state two constraints: a Markedness constraint that banslexical inversion, and the Faithfulness constraint violated by (32)b when (32)a is the underlyingrepresentation. This is the subject of the next two sections.

7.1.1 MATCH STRESS

In formulating a constraint to exclude lexical inversions, we are in well-explored territory.Kiparsky (1975), Bjorklund (1978), and other scholars have shown that poets and poetic

19 Three cases of lexical inversion in (4/G)3(4/G)3 I have noticed are Karpeles (1932):3B, Karpeles(1974):60G, and Karpeles (1974):72.


traditions often require a particularly strict match to the meter for sequences of stressed andunstressed syllables that fall within a single simplex word. Let us assume such a constrainthere:20

(33) MATCH STRESS

Assess a violation if:

• σi and σj (in either order) are linked to grid positions Gi and Gj respectively;• σi is more stressed than σj;• Gj is stronger than Gi; and• σi and σj occupy the same simplex word

In a full grammar, there would be other constraints requiring stress matching in othercontexts as well; but for present purposes (33) will suffice.

7.1.2 IDENT(location)

We must also formulate the Faithfulness constraint that is violated when, for example, (32)bis taken to be a candidate surface form for underlying (32)a. Here, the content of grid andphonological representation are identical, but the temporal association of syllables and gridmarks alignment is different. I will assume that this violates a Faithfulness constraint to becalled IDENT(location):

(34) IDENT(location)

If σi is linked to grid position G in the input, and to grid position G′ in the output candidate,assess a number of violations equal to the distance in grid positions between G and G′.

To make (34) explicit, we need to say how violations are assessed when more than one syllableis shifted over. Various possibilities exist; since nothing matters here in how this issue isresolved, I will assume for concreteness that the violations are simply summed. Thus (32)b,taken as a surface candidate for underlying (32)a, incurs 9 violations of IDENT(location): 2 forWil-, 2 for -liam, 2 for he, 2 for was, and 1 for a, as shown below:


| 2 | 2 | 2 | 2 | 1 | |*Wil- liam he was a noble knight (32)a

Wil- liam he was a noble knight (32)b

20 A constraint with this name is assumed in Hayes and MacEachern (1998), but there it takes the rather

artificial form “Prefer lines of type F”. Constraint (33) is by contrast well-supported elsewhere in metrics.


7.1.3 Ruling Out Nonfinal Lexical Inversion

The goal is to construct an analysis in which (32)a, with a lexical inversion in nonfinalposition, is unmetrical. Assume that (32)a is the underlying form, and that (32)b is a rivalcandidate. If MATCH STRESS outranks IDENT(location), (32)b will be the winner, as (36) shows.

(36) input form:(32)a William he was a noble knight

MATCH

STRESS

IDENT

(location)� (32)b William he was a noble knight 9 *’s

*(32)a William he was a noble knight *!

Because it is beaten by (32)b, (32)a is excluded from the output set and is unmetrical.

There is independent reason to think that the ranking MATCH STRESS >> IDENT(location)will prevail, because IDENT(location) is generally a weak constraint and MATCH STRESS a strongone. Here is the evidence for these two claims.

The experimental data gathered by HK indicate that folk song lines are composed in a waysuch that the grid locations of the syllables are relatively predictable. In particular, HK’sconsultants, given only text and grid, showed fair agreement among themselves as to what theproper alignment of syllables to grid should be. They could not have achieved this unless thesong texts gave them clues as to where to locate the syllables. This implies that where syllablesgo in the grid is, to a fair degree, noncontrastive information.

In Optimality-theoretic terms, noncontrastive structural information is that which isprotected by low-ranking Faithfulness constraints; hence, IDENT(location) must be ranked low.

On the other hand, MATCH STRESS is expected, based on our general knowledge, to beranked rather high. There are poetic traditions (e.g. classical German and Russian verse) inwhich it is undominated, and even where MATCH STRESS is violated there are usually strictlimitations on where the violations may occur (Kiparsky 1977). Moreover, quite a few folksongshave no lexical inversions at all, suggesting that they are composed under a ranking in whichMATCH STRESS is undominated (see §7.3 below). If rankings are relatively constrained evenacross different metrical forms, we expect MATCH STRESS to be ranked relatively high in general.It would certainly be expected to outrank a characteristically feeble constraint likeIDENT(location).

The upshot is that in the general case, candidates that match stress by “sliding” the syllableswill be favored over candidates that mismatch stress. This provides an across-the-board pressureagainst lexical inversion.


7.2 Ruling Out Non-Final Inversion

To explain why inversion can occur at the end of the line (in certain quatrain types), HKnote that in this location, additional constraints are active. These constraints rule out all of theavailable “slid over” candidates, leaving lexical inversion behind as the best remaining option.21

The way this works should be clear if we ponder what kind of syllable-sliding in principlecould rescue the lexical inversion in (37):


| | | | | | | | | |Fair El-li- nor she was a gay lady Karpeles 1974, 15I

The crucial stressed syllable la- must migrate to a stronger position than mismatched -dy. Themigration in principle could be to the left (where gay sits in (37)) or to the right (the location of-dy in (37)). For each of these two possibilities, there are two reasonable22 possibilities for whereto put -dy, making a total of four, shown in (38). The dotted arrows show where la- has been“moved” in each of the four possibilities.


| | | | | | | | | |Fair El-li- nor she was a gay lady original, with inversion

| | | | | | | |a. Fair El-li- nor she was a gay lady slide la- leftb. Fair El-li- nor she was a gay lady | slide la-, -dy leftc. Fair El-li- nor she was a gay la-dy slide la-, -dy rightd. Fair El-li- nor she was a gay la- slide la- right; -dy into

-dy… next line

Below, I consider the four possibilities in turn, and show that under appropriate constraintrankings, they are excluded. The lexical inversion setting remains as the most viable option.

21 This passage is alarmingly reminiscent of §1 above, in which it is argued that OT’s principle of always

outputting the best candidate can be a problem in metrics. As it turns out, it is possible to eat one’s cake and have ittoo. In the analyses that follow, we will see some forms emerging faute de mieux, as they should, and other casesappropriately yielding derivations that crash.

22 By “reasonable” I mean “without gratuitous violations of other constraints.”


7.2.1 Sliding to G

Example (38)a, repeated alone below as (39), is a candidate in which MATCH STRESS isobeyed by moving the penult of lady into the third strong position of the line, crowding some ofthe other syllables to fit it in. The syllable -dy is kept in the fourth position, so a G line results.


| | | | | | | | | |Fair El-li- nor she was a gay lady

This candidate will fail to defeat the lexical inversion candidate (37), provided that *LAPSE, theconstraint that forbids G, is ranked above MATCH STRESS:

(40) input form:(37) Fair Ellinor she was a gay lady

*LAPSE MATCH

STRESS

IDENT (location)

� (37) Fair Ellinor she was a gay lady **(39) Fair Ellinor she was a gay la——dy *! 9 *’s

As we will see in §7.4 below, this ranking will necessarily hold, for independent reasons, in thequatrain types that allow lexical inversion.

7.2.2 Sliding to 3f

Example (38)b, repeated as (41), is similar to (38)a: la- is again placed in the third strongposition of the line, but in this case -dy is also slid over, so that a 3f line results.


| | | | | | | | | |Fair El-li- nor she was a gay lady

If FILL STRONG, which forbids 3 and 3f lines, is ranked above MATCH STRESS, then this candidatewill also fail to defeat the lexical inversion candidate (37):


FILL

STRONG

MATCH

STRESS

IDENT (location)

� (37) Fair Ellinor she was a gay lady **(41) Fair Ellinor she was a gay lady ∅ *! 11 *’s


7.2.3 The Fast-Syllable Candidate

Example (38)c, repeated as (43), is a candidate in which la- has been moved rightward to thefourth strong position of the line; -dy occupies the weak terminal position.


| | | | | | | | | |Fair El-li- nor she was a gay la-dy

Impressionistically, the effect is of an uncomfortably fast rendition of lady at the end of the line,suggesting unmetricality. In fact, lines like this are quite rare in real verse. Moreover, in anexperiment conducted by HK, in which 670 lines of folk verse were chanted from the writtentext by 10 native speakers, the consultants fairly generally avoided this kind of rendition.

HK suggest that this line type is ill formed because it involves a gross mismatch of the sungduration of the final syllables versus their natural duration. (For discussion of the evidence thatsupports duration matching in folk verse, see HK §6.1.) In the present case, because of theeffects of phrase-final lengthening (Wightman et al. 1992), and the concurrence of line andintonation phrase boundaries, the line-final syllable is normally quite long. It is therefore illfitted to fill a single grid slot.

I will therefore assume a constraint to be called MATCH DURATION, which penalizesintonational phrase-final syllables23 that receive only one grid slot. I assume further that MATCH

DURATION is quite highly ranked, and in particular that it outranks MATCH STRESS. Therefore,the “fast syllable” candidate (43) (shown here iconically with condensed type) must lose out tothe inverted stress candidate (37):


MATCH

DURATION

MATCH

STRESS

IDENT

(location)� (37) Fair Ellinor she was a gay lady *

*(43) Fair Ellinor she was a gay lady *! 6 *’s

7.2.4 The Overflow Candidate

The fourth and last reasonable possibility for placing lady in metrically matched positionwas (38)d, repeated below as (45):

23 And possibly, other very long syllables as well; the issue is not crucial here.



| | | | | | | | |Fair El-li- nor she was a gay la-


|dy…

This setting, in which the second syllable of lady spills over into grid territory of the nextline, is a run-on line. This is unusual in folk verse, and arguably is so because it violates generalprinciples of alignment for phonological phrasing and metrical constituents. Evidence in supportof such alignment principles is given in Kiparsky (1975), Hayes (1989), Hayes and MacEachern(1996), and HK §6.2.

In the formal grammar, I assume that such lines violate Alignment constraints (McCarthyand Prince 1993), which in this case require line breaks to coincide with major phonologicalphrase breaks. For concreteness, I will assume that the relevant type of phrase break is theIntonational Phrase, though in a full grammar additional constraints would be needed that referto higher and lower prosodic domains as well (Selkirk 1980, Nespor and Vogel 1986,Pierrehumbert and Beckman 1986). In McCarthy and Prince’s terminology, the relevantconstraint is ALIGN(Line, L, Intonational Phrase, L): “the left edge of every Line must coincidewith the left edge of an Intonational Phrase.”

ALIGN(Line, L, Intonational Phrase, L) is a characteristically strong constraint in folk verse,and I assume it generally outranks MATCH STRESS. Under this ranking, candidate (45) must loseout to the lexical inversion candidate:


ALIGN MATCH

STRESS

IDENT

(location)� (37) Fair Ellinor she was a gay lady *

*(45) Fair Ellinor she was a gay la- ]Line [ dy *! 7 *’s

7.2.5 Result

Summarizing, candidates with lexical inversion will win when the inversion is in finalposition, and lose when the inversion is in other positions, if the following rankings hold:

(47) {*LAPSE, FILL STRONG, MATCH DURATION, ALIGN(Line, L, Intonational Phrase, L)} >>MATCH STRESS >> IDENT(location)


7.3 Songs Where Inversion is Illegal

A defect in this account is that it implies that any lexical inversion could be acceptable on afaute de mieux basis. The evidence from folk verse indicates that this is probably wrong. Manylong songs include no lexical inversions at all,24 and it is reasonable to suppose that such songsare composed under a ranking that classifies inversion candidates as completely ill formed.What might this ranking be?

We can posit here that the relevant ranking is MATCH STRESS >> MAX(σ). Under such aranking, a lexical inversion, even in final position, is defeated by a suicide candidate in which thestressless syllable is lost. One suicide candidate of this type is given in (48).


| | | | | | | | |*Fair El-li- nor she was a gay [le�d]

The following tableau shows how the suicide candidate defeats the inversion candidate:


otherconstraints

MATCH

STRESS

MAX

(σ)IDENT

(location)� (48) Fair Ellinor she was a gay [le�d] *

*(37) Fair Ellinor she was a gay lady *!

As before, the suicide candidate does not embody a legal line of verse, since it is excludedparaphonologically: nothing in English metrical paraphonology permits arbitrary dropping ofwhole syllables.

In verse that does allow (line-final) inversion, MAX(σ) must dominate MATCH STRESS.Under this ranking, (37) would be the winner; it would therefore belong to the output set andcount as metrical.25

This result may be related to the discussion above in §1. In their original account, HKassumed a naïve OT approach in which the best candidate always emerges as well formed. Inverse varieties that avoid lexical inversion, this assumption turns out to be wrong. The morearticulated version of OT used here, incorporating Faithfulness, componentiality, and suicidecandidates, is able to make the correct prediction of outright unmetricality.

24 Some examples (all 4343) are: Karpeles (1932), 31D, 42B, 97A, 186A; Karpeles (1974), 12A, 18G, 95C,

130A, 141B.25 A further detail: in verse types where lexical inversion is to be metrical line-finally, we must also rule out

suicide candidates that replace mismatched feminine endings with non-feminine endings by inserting a syllable, asin Fair Ellinor she was a gay lady O. This will follow if DEP(σ), which rules out such candidates, likewisedominates MATCH STRESS. This assumption will also hold for the discussion in §7.4 below.


7.4 Linking Inversion to Quatrain Type

It remains to account for one more of HK’s observations: that inversion is unusual in theodd numbered lines of (4/G)3(4/G)3 quatrains. The argument works as follows.

(1) Consider any pair of lines L4 and LG that have the same text but differ in that L4 is a 4line with a final lexical inversion and LG is a G line. For example, L4 could be (37) and LG couldbe (39). L4 and LG differ in their crucial Markedness violations: L4 violates MATCH STRESS (andLG does not); LG violates *LAPSE (and L4 does not). Moreover, since L4 and LG have the verysame text, there will be no Faithfulness violations other than IDENT(location) when L4 is taken asa candidate surface form for underlying /LG/ or vice versa.

(2) By hypothesis, the quatrain type is (4/G)3(4/G)3. Therefore, underlying G lines in thefirst and third lines must be able to defeat all alternative settings. For LG, this includes the rivalcandidate L4. Since L4 violates only the feeble IDENT(location) among the Faithfulnessconstraints, it must be the case that LG defeats L4 based on Markedness. Given the markednessconstraints that L4 and LG violate, it follows that MATCH STRESS must dominate *LAPSE.

(3) Lastly, consider what happens when L4 is the underlying form. Given what has just beensaid, L4 cannot survive into the output set, because LG will defeat it. Specifically, theFaithfulness constraint IDENT(location) is too weak to save L4, and the markedness constraintsMATCH STRESS and *LAPSE have just been shown to be ranked in a way that causes LG to defeatL4. The upshot is that if the constraints are ranked in a way that permits G lines to occur in freevariation with 4 lines, then lexical inversion candidates cannot make it into the output set, andare thus unmetrical.

The only exception will be when MATCH STRESS and *LAPSE are specially designated to befreely ranked. I assume that the relatively few cases where lexical inversion occurs in the oddlines of a (4/G)3(4/G)3 quatrain fall under this heading. However, even in this circumstance,there will be a complexity penalty for both inversion and G lines, for reasons discussed in thenext section.

8. Metrical Complexity

In the final section of this paper I will consider how the ideas presented here can be adaptedto bear on the question of metrical tension or complexity. For earlier work on metricalcomplexity, see Halle and Keyser (1966, 1971); Kiparsky (1975, 1977), Youmans (1989), andGolston (1998).

I adopt from Youmans’s work the position that metrical complexity should be analyzed inthe same terms as metricality; i.e. that absolute metricality and unmetricality are only the endpoints of a continuum. One reason to believe this is that, when one examines a variety of poetsand traditions, complexity turns out to respond to the same factors that govern metricality. Forinstance, the coincidence of a prosodic break with the post-4th position hemistich break of theiambic pentameter is a strong normative tendency for many English poets. For the verse of


George Gascoigne, however, or French pentameter (the “decasyllabe”), it is obligatory. Suchcases are easily multiplied.

The shared basis of metricality and complexity has a natural interpretation under OptimalityTheory: the traditions and poets differ not in the fundamental principles (constraints) that guideverse composition, but only in their constraint ranking.

If this view is correct, then what is needed for analyzing gradient well formedness is aconception under which ranking is a gradient phenomenon. For this purpose, I adopt theapparatus developed in HM, Hayes (in press) and Boersma and Hayes (in press). The version ofBoersma and Hayes is the most quantitatively explicit, and will be employed here.

In this model, constraints are assigned ranking values on a continuous numerical scale.Grammars are stochastic, in that at any one application of the grammar (e.g., the composition ofa single quatrain), the values employed for constraint strictness are determined at random. Thisis done by selecting a point for each constraint from a normal probability distribution, centeredon its ranking value. Grammars of this type can generate a range of outcomes, with differentprobabilities affiliated with each outcome, depending on the ranking values of the constraints.However, such grammars can also generate outcomes that are essentially categorical; this occurswhen the ranking values of the relevant constraints are extremely far apart.26

A crucial further assumption of the model is that, at least in the crucial class of cases,gradient well-formedness can be treated in terms of probability: forms that could be derivedonly under a somewhat unlikely choice of selection points are assumed to be somewhat ill-formed; forms that could derived only under a highly unlikely choice of selection points areassumed to be almost entirely ill-formed, and so on.

This model of gradient well formedness has been tested by Boersma and Hayes against dataon English /l/, taken from Hayes (in press); and against data involving the nasal mutation processof Tagalog by Zuraw (2000). In both cases, the model achieves a good match against scalarwell-formedness judgments gathered from a panel of native speakers. A similar, though non-quantitative, model has been used in metrics by HM to describe certain quatrain types (such as333f3) that are semi-ill-formed.

In the present case, we need to adapt the stochastic apparatus to inventory grammars, whichdesignate whether a representation is or is not in an output set. Adapting the probability-basedstrategy just described, I posit that the appropriate definition of complexity is as follows:

26 I use the word “essentially” because the relevant type of grammar will generate certain forms with

extremely low probability. If this probability is low enough, say, one in a million, then these rare outcomes couldnot be distinguished empirically from performance errors, and thus could not sensibly be counted as wrongpredictions.


(50) Metrical Complexity

The metrical complexity of a line (couplet, etc.) is defined as the probability that theconstraints of a stochastic OT grammar will be ranked in a way that excludes it from theoutput set.

On this scale, the complexity of a line or other structure varies from 0 (under all possiblerankings of the grammar, the line will be allowed in the output set) to 1 (there is no possibleranking that allows it in the output set). The value 0 is equivalent to perfect metricality, and thevalue 1 is equivalent to total unmetricality.

Obviously, (50) is a theory-internal definition of complexity. Complexity is also a term thatis defined empirically, relating to the gradient intuitions people have about verse structures. Myhypothesis is that with appropriate constraints and rankings, the probability-based theoreticalvalues defined by (50) can be mapped onto human intuitive judgments by some monotonicfunction. Plainly, extensive research would be needed to test this claim.

However, definition (50) can already be seen to have three advantages. First, it isquantitatively explicit. Second, it is compatible with the criterion set above for an adequatetheory of complexity; i.e. that metricality and unmetricality should be characterized as extremes(here, 0 and 1) on the complexity continuum. Finally, under this approach, the samemechanisms—constraints—are used to characterize both metricality and complexity.

8.1 The Complexity of Inversion

A good example of metrical complexity in folk verse is lexical inversion, analyzed in §7above. I think most listeners share a sense that lines with inversion are complex; certainly it hasattracted the attention of the scholars who have examined folk verse; cf. Hendren (1936, 137);Karpeles (1973, 24). Experimental evidence also supports the complexity of inversion: theconsultants for Hayes and Kaun (1996), asked to chant texts that in the original song included aninversion, often responded with alternative non-inverted settings, but seldom did the reverse.27

I will now attempt to characterize inversion quantitatively as complex. Specifically, I willdevelop a grammar in which lines containing lexical inversion will emerge with a complexityvalue no lower than .8. This value is arbitrary, being unanchored in experimental data; the pointis to show that the grammatical apparatus is capable of providing such values.

I will assume that the quatrain type under examination is always of the type 4343. Thisquatrain type can be guaranteed by the (essentially) strict rankings given below:

27 The numbers are as follows: in 74/170 cases, consultants presented with the text of lines that contained

line-final inversions in the original responded with a non-inverted setting. In 790 cases, consultants were presentedthe text of a line that had a feminine ending but was not inverted in the original; of these, they replied with aninverted rendering only 26 times. Thus the “uninversion” rate was 43.5%, whereas the “spontaneous inversion” ratewas only 3.3%.


(51) COUPLETS ARE SALIENT

13.49 units higher than 13.49 units higher than

FILL STRONG *LAPSE

13.49 units higher than 13.49 units higher than

LINES ARE SALIENT

The units along the strictness scale are as defined in Boersma and Hayes (in press). The value13.49 is chosen as that which results in a one-in-a-million probability against a reversed rankingfor the arrows shown; hence, these ranking are essentially obligatory.28

The ranking arguments for (51) are as follows: COUPLETS ARE SALIENT must outrank FILL

STRONG if 4343 is to defeat 4G4G, or any other quatrain type that fills the last strong position ofa couplet. COUPLETS ARE SALIENT must outrank *LAPSE if 4343 is to defeat 43f43f. FILL

STRONG must outrank LINES ARE SALIENT if 4343 is to defeat 3f33f3, and *LAPSE must outrankLINES ARE SALIENT if 4343 is to defeat G3G3.

A second, independent group of rankings is the following (their relative placement along thescale with respect to the constraints of (51) would not matter):

(52) {MATCH DURATION, ALIGN(Line, L, Intonational Phrase, L)}

13.49 units higher than

MATCH STRESS

2.38 units higher than13.49 units higher than

MAX(σ)

IDENT(location)

The (essentially) categorical rankings MATCH DURATION >> MATCH STRESS, ALIGN >>MATCH STRESS, and MATCH STRESS >> IDENT(location) are defended above, in §7.2.3, §7.2.4,and §7.1.3 respectively. The crucially gradient ranking is MATCH STRESS >> MAX(σ). Whenthe math is worked out, it emerges that with the difference of 2.38 in ranking values shown, thereis an 80% probability that MATCH STRESS will dominate MAX(σ) at any given evaluation time.As we saw in §7.3, when MATCH STRESS dominates MAX(σ), inverted lines are defeated in the

28 An explanation of how probabilities are derived from ranking value differences may be found in Zuraw

(2000).


candidate competition by suicide candidates that remove the final unstressed syllable of the line.Therefore, under the gradient ranking of (52) there is an 80% probability that a candidate withfinal inversion will not make it into the output set. The metrical complexity of lines withinversion (all else in the line being perfect) is thus .8, which is what we sought originally todescribe.

8.2 Complexity in General

This analytic strategy can be extended to serve as a treatment of metrical complexity ingeneral, in the following way.

Suppose we want to characterize the complexity of a given metrical structure S in thegrammar. We locate first a markedness constraint M violated by lines (quatrains, etc.)containing S. We also locate a distinct structure S′, such that lines containing S′ instead of Sobey M, but violate a Faithfulness constraint F, and moreover are paraphonologically illegal.Under these circumstances (all else being equal), lines containing S will be:

• Unmetrical if M outranks F by a wide margin.• Metrical but complex if M and F have relatively close ranking values. The degree of

complexity will depend on the size and direction of the difference.• Fully metrical if F outranks M by a wide margin.

It is these rankings that determine the likelihood of whether lines containing S can survive thecompetition with a suicide candidate that contains S′ instead of S.

In the case discussed in §8.1, S was the mismatched lady in (37), S′ was the correspondingmaterial ([le�d]) in (48), M was MATCH STRESS, and F was MAX(σ). In other instances, thecrucial Faithfulness constraint could in principle be different; for example DEP(σ), Faithfulnessto prosodic phrasing, or Faithfulness to the input stress pattern.

9. Conclusion

Optimality Theory appears to have major potential advantages as an approach to metrics. Itachieves explanatory force by letting the “ingredients” of metrical grammars be general,typologically motivated constraints, with idiosyncrasy resulting from genre- or tradition-specificconstraint rankings. Moreover, existing case studies, such as the analysis of quatrains in Hayesand MacEachern (1998) or of lexical inversion in Hayes and Kaun (1996), indicate that the datapatterns seen in metrics really do reflect constraint conflict. In the introduction to this paper, Ilaid out four problems involved with deploying OT in metrics. To conclude, I will review thesolution proposed here for each problem.

The first problem was that metrics is not the mapping of one representation onto another;rather, it involves the enumeration of a set of legal structures. The proposed solution is to do thisby letting an OT grammar act as a filter on a rich base; this is the concept of an inventorygrammar.


The second problem was that lines can be unmetrical without suggesting a metricalalternative. The proposed solution was to follow Kiparsky’s (1977) view that metrics iscomponential. In a componential system, suicide candidates arise, which can exclude formsfrom the output set but are not themselves metrical.

The third problem was how constraint violations are related to unmetricality. The proposedsolution, as elsewhere in OT, is based on the relative ranking of Markedness and Faithfulness. AMarkedness constraint M will be effective in ruling out a form if it outranks the Faithfulnessconstraints that are violated by the relevant suicide candidates.

The final problem was how constraint violations can be related to complexity; and morespecifically, how we can characterize complexity when there exist forms that sound perfect yetviolate many constraints. The proposed solution invokes the theory of stochastic OT grammars:complexity is not the direct result of constraint violation, but rather of improbably high rankingsof Faithfulness over Markedness.


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Youmans, Gilbert. 1989. Milton’s meter. In Kiparsky and Youmans (1989), pp. 341-379.Zuraw, Kie (2000). Exceptions and Regularities in Phonology. Doctoral dissertation, UCLA,

Los Angeles, CA.

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